I think you will find the terminology on TERPS SIDS are "climb on runway heading". Believe it or not this means TRACK. Its written not spoken.
Now.... completely different situation; A controller says "fly runway heading" (only in FAA influenced areas I think we all agree). This, as someone has already pointed out, means put the runway heading at the top of your HSI. Except in Japan, where you fly the cardinal number at the top of your HSI. A good example of just how silly that idea has become is New Chitose Airport. Runway 19 (direction is 182) if instructed to 'Fly runway heading' you fly 190. The Japanese think its simple!!!!!! Why do we not?
Just to muddy the water now... Were we all not taught in our primary training around the circuit to track the extended centreline of the runway? We were on runway heading then.. no?